dismay vs despair

dismay and despair both are nouns.

Word	Noun	Adjective	Verb	Adverb
dismay	Yes	No	Yes	No
despair	Yes	No	Yes	No

As nouns, despair is a hypernym of dismay; that is, despair is a word with a broader meaning than dismay:

dismay: the feeling of despair in the face of obstacles
despair: the feeling that everything is wrong and nothing will turn out well

dismay (noun)	despair (noun)
fear resulting from the awareness of danger	the feeling that everything is wrong and nothing will turn out well
the feeling of despair in the face of obstacles	a state in which all hope is lost or absent

dismay (verb)	despair (verb)
fill with apprehension or alarm; cause to be unpleasantly surprised	abandon hope; give up hope; lose heart
lower someone's spirits; make downhearted